US10317498B2 - Methods and apparatus for modeling diffusion-weighted MR data acquired at multiple non-zero B-values - Google Patents
Methods and apparatus for modeling diffusion-weighted MR data acquired at multiple non-zero B-values Download PDFInfo
- Publication number
- US10317498B2 US10317498B2 US15/022,343 US201415022343A US10317498B2 US 10317498 B2 US10317498 B2 US 10317498B2 US 201415022343 A US201415022343 A US 201415022343A US 10317498 B2 US10317498 B2 US 10317498B2
- Authority
- US
- United States
- Prior art keywords
- diffusion
- compartment
- model
- weighted
- data
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active, expires
Links
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
- G01R33/48—NMR imaging systems
- G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
- G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
- G01R33/563—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution of moving material, e.g. flow contrast angiography
- G01R33/56341—Diffusion imaging
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves
- A61B5/055—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves involving electronic [EMR] or nuclear [NMR] magnetic resonance, e.g. magnetic resonance imaging
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
- G01R33/48—NMR imaging systems
- G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
- G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
- G01R33/5608—Data processing and visualization specially adapted for MR, e.g. for feature analysis and pattern recognition on the basis of measured MR data, segmentation of measured MR data, edge contour detection on the basis of measured MR data, for enhancing measured MR data in terms of signal-to-noise ratio by means of noise filtering or apodization, for enhancing measured MR data in terms of resolution by means for deblurring, windowing, zero filling, or generation of gray-scaled images, colour-coded images or images displaying vectors instead of pixels
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B2576/00—Medical imaging apparatus involving image processing or analysis
- A61B2576/02—Medical imaging apparatus involving image processing or analysis specially adapted for a particular organ or body part
- A61B2576/026—Medical imaging apparatus involving image processing or analysis specially adapted for a particular organ or body part for the brain
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
- G16H30/00—ICT specially adapted for the handling or processing of medical images
- G16H30/40—ICT specially adapted for the handling or processing of medical images for processing medical images, e.g. editing
Definitions
- Magnetic resonance imaging includes techniques for capturing data related to the internal structure of an object of interest, for example, by non-invasively obtaining images of internal structure of the human body, and has been widely used as a diagnostic tool in the medical community.
- MRI exploits the nuclear magnetic resonance (NMR) phenomenon to distinguish different structures, phenomena or characteristics of an object of interest.
- NMR nuclear magnetic resonance
- MRI may be employed to distinguish between various tissues, organs, anatomical anomalies (e.g., tumors), and/or to image diffusion, blood flow, blood perfusion, etc.
- MRI operates by manipulating spin characteristics of subject material.
- MRI techniques include aligning the spin characteristics of nuclei of the material being imaged using a generally homogeneous magnetic field and perturbing the magnetic field with a sequence of radio frequency (RF) pulses.
- RF radio frequency
- one or more resonant coils may be provided proximate an object positioned within the magnetic field.
- the RF coils are adapted to generate RF pulses, generally in the form of RF pulse sequences adapted for a particular MRI application, to excite the nuclei and cause the spin to process about a different axis (e.g., about an axis in the direction of the applied RF pulses).
- spins gradually realign with the magnetic field, releasing energy that can be measured to capture NMR data about the internal structure of the object.
- MR-DWI magnetic resonance diffusion-weighted imaging
- TE is the echo time
- T2 is the T2 relaxation time of the tissue
- ⁇ is the gyromagnetic ratio
- ⁇ and ⁇ are the diffusion sensitizing pulse gradients duration and time separation
- D is the 3 ⁇ 3 diffusion tensor.
- the nominal b-value b nominal ⁇ 2 ⁇ 2 ( ⁇ /3) describes the b-value for the unit-norm gradients.
- the term e ⁇ TE/T2 is generally considered constant across all gradients and omitted. However, and importantly, this term highlights how the signal amplitude S k (D) decreases exponentially for increasing TE.
- DTI and its underlying mono-exponential signal attenuation assumption are generally considered to satisfactorily represent single fascicles when imaging with b-values lower than 3000 s/mm 2 , which is frequently the case in clinical settings.
- Non-monoexponential behavior of the signal at a voxel in this b-value range can arise from cerebral spinal fluid (CSF) partial voluming, mixtures of fascicles present in the voxel, and other sources.
- CSF cerebral spinal fluid
- the diffusion tensor enables representation of the orientation of a single fascicle, as well as the characterization of the diffusion process.
- Tensor parameters such as the fractional anisotropy (FA), the mean diffusivity (MD), the axial diffusivity (AD), and the radial diffusivity (RD) can be computed, and have been shown to provide valuable information that reflects changes in the white matter due to development, disease and degeneration. DTI requires relatively short acquisition times and has been successfully employed in clinical studies.
- FA fractional anisotropy
- MD mean diffusivity
- AD axial diffusivity
- RD radial diffusivity
- DTI has been shown to be a poor parametric model for representing the diffusion signal arising at voxels that encompass multiple fascicles with heterogeneous orientation such as fascicle crossing, kissing or fanning.
- Cartesian sampling and spherical sampling are two q-space sampling strategies that have been used for complex fiber structure assessment.
- Cartesian sampling is used by diffusion spectrum imaging (DSI).
- Spherical sampling as employed in high angular resolution imaging (HARDI) techniques reduces the imaging time and requires imaging gradients with moderate intensity.
- HARDI-based techniques have been proposed, as discussed in further detail below.
- Single-shell HARDI acquisitions with a single non-zero b-value have been considered to image a sphere of constant radius in q-space.
- Multiple-shell HARDI acquisitions that enable the acquisition of multiple non-zero b-values by combining in a single acquisition, the sampling of multiple shells of different radius in q-space, have also been proposed.
- sampling using the tetrahedral ⁇ square root over (3) ⁇ -norm gradients has been employed to measure the apparent diffusion coefficient (ADC) from four diffusion measurements.
- ADC apparent diffusion coefficient
- the six hexahedral ⁇ square root over (2) ⁇ -norm gradients may be used to estimate a diffusion tensor from seven measurements. Furthermore, in (CUbe Rays to Vertices and Edges) CURVE-ball, a spherical sampling and the hexahedral and tetrahedral gradients are combined to perform the estimation of a single-tensor model at three different diffusion scales b nominal , 2b nominal , and 3b nominal .
- Model-free approaches include diffusion spectrum imaging (DSI).
- DSI diffusion spectrum imaging
- the diffusion PDF is directly estimated from the inverse Fourier transform of the measured signal, requiring a very high number of measurements to satisfy the Nyquist condition.
- Q-ball imaging (QBI) estimates an approximate non-parametric angular profile of the diffusion PDF without actually computing the diffusion PDF, by using the Funk-Radon transform.
- Fast and robust analytical QBI estimation procedures have been proposed.
- QBI results in the estimation of an approximated dODF related to the true dODF by modulation with a zero-order Bessel function. This leads to a spectral broadening of the diffusion peaks of individual fascicles at moderate b-values accessible on a clinical scanner, perturbing the FOD reconstruction necessary for carrying out tractography.
- EQBI Exact Q-Ball Imaging
- Q-space approaches such as DSI, QBI, or EQBI are limited by at least three error sources. These techniques are based on the narrow pulse approximation assumption, considering that molecules do not diffuse during the application of the diffusion sensitizing gradients.
- the gradient pulses are then modeled by a Dirac shape which is not practically feasible, especially on clinical systems.
- the diffusion-encoding gradient duration ⁇ is typically of the same order of magnitude as the time offset ⁇ between encoding gradients ( ⁇ / ⁇ 1) to minimize T2 decay and to obtain better SNR, which is a very poor approximation of a Dirac shape. Additionally, since the imaging time has to be finite, only a finite region in q-space is imaged using these techniques.
- GDTI generalized diffusion tensor imaging
- SD spherical deconvolution
- DOT diffusion orientation transform
- Some embodiments include a system for characterizing biological microstructure in a voxel based, at least in part, on a plurality of diffusion-weighted images.
- the system comprises at least one computer processor and at least one storage device configured to store a plurality of instructions that, when executed by the at least one computer processor, perform a method of fitting a novel parametric model using information from a set of diffusion-weighted data.
- the novel parametric model describes statistical distributions of 3-D diffusivity arising from each of a plurality of tissue compartments for the voxel.
- the complexity of the parametric model may be increased by adapting the parametric model to account for additional compartments, such that the parametric model is capable of modeling parameters for the set of diffusion-weighted data from one to N compartments.
- the first compartment models free or restricted isotropic diffusion, and at least one subsequent compartment models restricted or hindered anisotropic diffusion by assuming presence of one or more white matter fascicles in the voxel.
- fitting the parametric model comprises determining, based on the set of diffusion-weighted MR data, a first set of parameters describing isotropic diffusion in a first compartment of the multi-compartment model and a second set of parameters describing anisotropic diffusion due to the presence of at least one white matter fascicle in a second compartment of the multi-compartment model, wherein at least one first dataset of the set of diffusion-weighted MR data is associated with a first non-zero b-value and at least one second dataset of the set of diffusion-weighted MR data is associated with a second non-zero b-value different than the first non-zero b-value.
- Some embodiments include determining the number of compartments to be modeled by the parametric model by minimizing a generalization error resulting from using the parametric model with N ⁇ 1 compartments and selecting the parametric model with the number of compartments with the smallest generalization error.
- the parametric model utilized for a given voxel may be adapted according to the number of white matter fascicles believed to be present in the voxel such that the complexity of the model fits the microstructure within the voxel appropriately.
- Some embodiments are directed to a computer system for characterizing biological microstructure in a voxel based, at least in part, on a set of diffusion-weighted magnetic resonance (MR) data.
- the computer system comprises at least one computer processor and at least one storage device configured to store a plurality of instructions that, when executed by the at least one computer processor, perform a method.
- the method comprises fitting a parametric model using information from the set of diffusion-weighted MR data, wherein the parametric model is a multi-compartment model, and wherein fitting the parametric model comprises determining for the voxel, based on the set of diffusion-weighted MR data, a first set of parameters describing isotropic diffusion in a first compartment of the multi-compartment model and a second set of parameters describing anisotropic diffusion due to the presence of at least one white matter fascicle in a second compartment of the multi-compartment model, wherein at least one first dataset of the set of diffusion-weighted MR data is associated with a first non-zero b-value and at least one second dataset of the set of diffusion-weighted MR data is associated with a second non-zero b-value different than the first non-zero b-value, and outputting an indication of the first set of parameters and/or the second set of parameters for the voxel.
- Some embodiments are directed to a method of characterizing biological microstructure based, at least in part, on a set of diffusion-weighted magnetic resonance (MR) data.
- the method comprises receiving the set of diffusion-weighted MR data, wherein at least one first dataset of the set of diffusion-weighted MR data is associated with a first non-zero b-value and at least one second dataset of the set of diffusion-weighted MR data is associated with a second non-zero b-value different than the first non-zero b-value; fitting, by at least one computer processor, a parametric model using information from the set of diffusion-weighted MR data, wherein the parametric model is a multi-compartment model, and wherein fitting the parametric model comprises determining for a voxel, based on the set of diffusion-weighted MR data, a first set of parameters describing isotropic diffusion in a first compartment of the multi-compartment model and a second set of parameters describing anisotropic
- Some embodiments are directed to a non-transitory computer readable storage medium encoded with a plurality of instructions that, when executed by at least one computer processor, perform a method.
- the method comprises fitting a parametric model using information from the set of diffusion-weighted MR data, wherein the parametric model is a multi-compartment model, and wherein fitting the parametric model comprises determining for a voxel, based on the set of diffusion-weighted MR data, a first set of parameters describing isotropic diffusion in a first compartment of the multi-compartment model and a second set of parameters describing anisotropic diffusion due to the presence of at least one white matter fascicle in a second compartment of the multi-compartment model, wherein at least one first dataset of the set of diffusion-weighted MR data is associated with a first non-zero b-value and at least one second dataset of the set of diffusion-weighted MR data is associated with a second non-zero b-value different than the first
- FIG. 1 illustrates the concept of non-monoexponential decay of signal with b-value detected in a voxel in a multi-fascicle model
- FIG. 2 illustrates multiple scales of intra-voxel heterogeneity that may be modeled in accordance with some embodiments
- FIG. 3 schematically illustrates parametric model representations that account for intra-voxel heterogeneity in accordance with some embodiments
- FIG. 4 illustrates a cross-section of the density for symmetric positive-definite (SPD) matrices whose off-diagonal entries are equal to zero;
- FIG. 5 shows a plot of angular detection accuracy for a ball-and-stick model and a novel DIAMOND model used in accordance with some embodiments
- FIG. 6 shows simulation results comparing the NODDI model and a novel DIAMOND model used in accordance with some embodiments
- FIG. 7 shows plots of parameters for various microstructures determined using variations of the NODDI model and a novel DIAMOND model used in accordance with some embodiments
- FIG. 8 shows a comparison of different diffusion models with in-vivo data by assessing their generalization error
- FIG. 9 shows a reconstruction of an image from high-resolution super-resolved DWI data using a novel DIAMOND model in accordance with some embodiments
- FIG. 10 shows a reconstruction of an image of a patient with Tuberous Sclerosis Complex (TSC) using a novel DIAMOND model in accordance with some embodiments;
- TSC Tuberous Sclerosis Complex
- FIG. 11 shows an illustrative process for iteratively fitting a generative model to diffusion-weighted MR data in accordance with some embodiments
- FIG. 12 is an exemplary computer system on which some embodiments may be implemented.
- FIG. 13 illustrates a MR scanning device suitable for obtaining DW-MRI data in accordance with some embodiments.
- a drawback of several of the diffusion-based modeling techniques described above is that they focus on describing the general shape of the diffusion profile in each voxel. They do not represent each fascicle independently and therefore do not characterize the proportion of each fascicle passing through a voxel. Importantly, they do not enable characterization of each fascicle. Diffusion parameters such as the generalized fractional anisotropy (GFA) can be computed, but represent a DW signal dispersion property rather than an individual fascicle property.
- GFA generalized fractional anisotropy
- a synthetic fascicle consisting of an identical tensor at every voxel crossed by another synthetic fascicle has a GFA that varies in the crossing region, which is not clinically relevant.
- multi-fascicle models consider, at each voxel, a mixture of independent fascicles with heterogeneous orientation. Making the assumption of a slow exchange between the fascicles' compartments, the diffusion signal in each voxel is modeled as a mixture of the diffusion signal arising from each individual fascicle. Integration of an isotropic component has also been investigated to model the diffusion of unrestricted water. This enables characterization of pathologies such as edema, stroke, or inflammation. This also enables characterization of the CSF contamination due to partial volume effect, known to perturb the accurate estimation of the anisotropic diffusion compartments.
- the diffusion-weighted signal S k along a gradient direction g k for MFM with an isotropic compartment and N f fascicles can be described by the following general mixture;
- S k,j single _ fascile is the diffusion signal arising from a single fascicle
- S k free _ water is the diffusion signal arising from the unrestricted water diffusion
- f (f 0 , . . . , f N f ) describes the fractions of occupancy of each compartment (f j ⁇ [0,1]) and sum to one.
- each individual fascicle is represented by a stick in the expression of S k,j single _ fascile .
- the ball-and-stick model provides information only about the fascicles' orientation, but does not enable the assessment of fascicle properties such as the fascicle anisotropy and diffusivity, limiting the use of the ball-and-stick model to connectivity studies.
- the spatial resolution of diffusion-weighted imaging is typically on the order of 6-27 mm 3 .
- the measured DW signal in each voxel combines the signal arising from a variety of microstructural environments including multiple cell types, sizes, geometries and orientations and extra-cellular space.
- a non-monoexponential decay may be observed in voxels when imaging with high b-values, providing evidence that the single tensor model and its underlying Gaussian assumption is not appropriate to accurately represent the diffusion signal in the voxel.
- the biophysical mechanisms responsible for the non-monoexponential behavior are, however, numerous and not completely understood. It is commonly recognized that compartmentalization of the voxel in different subregions with heterogeneous properties can lead to a non-monoexponential decay under certain acquisition conditions.
- FIG. 1 illustrates that intra-voxel orientation heterogeniety and partial volume averaging leads to a non-monoexponential decay in a voxel.
- FIG. 1 illustrates that intra-voxel orientation heterogeniety and partial volume averaging leads to a non-monoexponential decay in a voxel.
- Models have been proposed to account for the observed non-monoexponential decay, including fitting a multi-exponential model and a “stretched-exponential model.”
- the estimation of a Kurtosis term which is a dimensionless measure of the deviation of the water diffusion profile from a Gaussian distribution, has also been investigated. These models attempt to describe the signal arising from each entire voxel and focus on capturing the mathematical deviation from the monoexponential decay.
- DCI diffusion compartment imaging
- CHARMED composite hindered and restricted model of diffusion
- NODDI neurite orientation dispersion and density imaging
- non-monoexponential decay for an individual fascicle is commonly accepted when using very high b-values and a short gradient pulse duration ⁇ , its presence in data acquired with a clinical scanner with limited b-value range and large remains unclear.
- the non-monoexponential behavior may be negligible when considering b-values lower than b ⁇ 3000 s/mm 2 , and when the acquisition time or the available gradient strength is limited, a monoexponential per-fascicle model may be safely employed.
- FIG. 2A illustrates that large-scale heterogeneity includes the mixing of large-scale microstructural environments (LSME), also referred to as compartments, such as the mixing of multiple WM fascicles with extra-cellular space.
- Large-scale heterogeneity also originates from partial volume averaging such as occurs when cerebrospinal fluid, gray matter and/or white matter are present in a voxel.
- each large-scale microstructural environment may contain a complex varying microstructure including axons with varying radii and degrees of myelination, or fascicles with a varying density of glial cells such as astrocytes and oligodendrocytes. It is likely that water molecules interacting with an homogeneous portion of this structure are well modeled by an exponential. However, the overall signal arising from the compartment may significantly deviate from a mono-exponential decay in the presence of heterogenity of the spin packets composing the compartment.
- FIG. 2C shows that at an even smaller scale, other biophysical mechanisms such as intracellular heterogeneities and the proximity of cell membranes may locally restrict water molecule motion and contribute to the signal decay behavior.
- the frog oocyte has been observed (Ax: axons with various degrees of myelination; As: Astrocyte; O: Oligodendrocyte).
- S k is the measured diffusion signal for the b-value b k
- S 0 is the signal with no diffusion applied
- P(D) is a probability distribution that describes the fraction of spin packets with an ADC D in the voxel, as shown in FIGS. 3 a - c .
- This statistical model of the ADC reflects, via the shape of the scalar-valued distribution P(D), the overall diffusivity and heterogeneity in each voxel.
- P(D) is a probability distribution that describes the fraction of spin packets with an ADC D in the voxel, as shown in FIGS. 3 a - c .
- This statistical model of the ADC reflects, via the shape of the scalar-valued distribution P(D), the overall diffusivity and heterogeneity in each voxel.
- P(D) is a probability distribution that describes the fraction of spin packets with an ADC D in the voxel, as shown in FIG
- FIG. 3 a illustrates a hypothetical isotropic two-population (or two-compartment) environment.
- FIG. 3 b shows that under the hypothesis of purely homogeneous compartments with no exchange, a bi-exponential decay is traditionally considered to describe the signal arising from the isotropic two-population environment of FIG. 3 a .
- the probability density of diffusivities represents the fraction of all possible ADCs present in the voxel.
- the probability density of diffusivities consists of two Diracs representing the ADC of each compartment.
- FIG. 3 c illustrates another technique in which each compartment is considered to have some degree of heterogeneity. In this technique, a peak-shaped continuous distribution of ADCs is used for each compartment, with the heterogeneity of a compartment being captured by the concentration of the corresponding peak.
- a 1-D gamma distribution model of diffusivities has been incorporated in the ball-and stick model, described above.
- the sticks only model the parallel intra-axonal diffusivity for each fascicle and the gamma distribution is mostly used to improve the fitting and to reduce overfitting.
- a parametric model may predict the diffusion signal using four compartments to respectively represent 1) freely diffusing water, 3) isotropic restricted diffusion water, 3) water molecules restricted to the intra-axonal space and 4) water molecules hindered by axonal membranes.
- which parameterization best describes the non-monoexponential signal arising from each tissue compartment remains an open problem.
- equation (3) can be generalized by modeling the tridimensional diffusivity of each spin packet with a full diffusion tensor D, as shown in FIGS. 3 d - f .
- this technique is analytically challenging because it implies the integration of a matrix-variate distribution P(D) over the space of tensors, which are symmetric positive-definite (SPD) matrices.
- SPD symmetric positive-definite
- mv- ⁇ matrix-variate Gamma
- FIG. 3 d shows a hypothetical multi-compartment model, in which an isotropic (v) and two anisotropic (iv and iii) compartments are mixed.
- v isotropic
- iv and iii anisotropic
- FIG. 3 e shows that under the hypothesis of purely homogeneous compartments with no exchange, a multi-tensor model is typically employed to describe the signal arising from environment of FIG. 3 d .
- the corresponding probability density of diffusivities is composed of a mixture of delta functions.
- FIG. 3 f shows a novel model called “DIAMOND,” discussed in more detail below, which captures the multidimensional diffusivity and heterogeneity of each compartment using peak-shaped distributions of multidimensional diffusivities.
- the expectation of each matrix-variate distribution captures the compartment overall diffusivity while the distribution concentration captures its microstructural heterogeneity. Specifically, a distribution with a broad peak indicates a highly heterogeneous compartment.
- Some embodiments are directed to using a parametric model to predict a diffusion signal represented in diffusion-weighted data, wherein the parametric model is based on a 3-D generalization of equation (3).
- ADCs are extended to be diffusion tensors, and each population of 3-D diffusivities (tensors) is described with a matrix-variate Gamma distribution.
- such an approach explicitly models the signal arising from each tissue compartment, and represents a model of the tissues. It enables assessment of the mean, axial and radial diffusivity of each compartment separately (cMD, cAD, cRD) and provides a measure of heterogeneity for each compartment.
- Some embodiments are directed to a novel DCI technique that characterizes the distribution of 3-D anisotropic microstructural environments in diffusion-compartment imaging (referred to as “DIAMOND” herein). Measurements arising from a large number of 3-D spin packets are considered such that each homogeneous spin packet undergoes local anisotropic 3-D diffusion represented by a diffusion tensor D. Each voxel may be assumed to contain heterogeneous populations of heterogeneous spin packets, and each population may be described with a mv- ⁇ distribution of spin packets. The signal at each voxel may be modeled by mathematical integration of the contributions of each 3-D spin packet, which has an analytical solution.
- DIMOND diffusion-compartment imaging
- a priori information about the expected shape of the spin packets distribution can be introduced to represent free, isotropically restricted, intra-axonal, and hindered diffusion arising from each white matter fascicle in each voxel.
- results obtained using the novel DCI technique described herein have been compared with numerous in-silico and in-vivo experiments and with pathological DW-MRI, as described in more detail below. These comparisons demonstrate that the angular error of DIAMOND favorably compares to other approaches such as the ball-and-stick model, described above. Insight into the model parameters of DIAMOND via various numerical simulations of tissue microstructures, such as varying axonal radius and varying fascicle dispersion, are also discussed below. These simulations show that DIAMOND better predicts the DW signal compared to NODDI, with both simulations and in-vivo data, providing evidence that DIAMOND better captures the underlying DW signal formation. DIAMOND may also provide novel biomarkers reflecting the tissue integrity, as discussed in more detail below.
- DIAMOND an Illustrative Generative Model for Diffusion-Based Imaging
- some embodiments relate to a novel technique for modeling diffusion-weighted data with a generalized parametric model that more accurately characterizes the tissue microstructures in each voxel.
- measurements of the DW signal arising from the large number of spin packets within a voxel are considered. Spin packets travel along different trajectories and are confronted with different barriers to displacement.
- Three-dimensional spin-packets are considered so that when interacting with an homogeneous portion of the microstructure these spin-packets give rise to anisotropic 3-D Gaussian diffusion represented by a diffusion tensor D, whose contribution to the signal for a diffusion gradient g k is: S 0 exp( ⁇ b k g k T Dg k )dD.
- D diffusion tensor
- Sym + (3) is the set of 3 ⁇ 3 SPD matrices.
- each microstructural environment contains some degree of heterogeneity, and is more appropriately described by a population of spin packets. This can be accounted for by modeling the composition of each microstructural environment with a peak-shaped matrix-variate distribution of spin packets centered around D 0 and defined over the space of SPD matrices, as shown in FIG. 3 f.
- the horizontal and vertical axes are the first and second diagonal entries of D, respectively.
- a p ⁇ p SPD random matrix D ⁇ Sym + (p) follows a mv- ⁇ distribution with shape parameter ⁇ >(p ⁇ 1)/2 and scale parameter ⁇ Sym + (p) if it has density:
- the shape parameter ⁇ determines the concentration: for constant D 0 , the density becomes more concentrated around D 0 as ⁇ increases.
- the presence of N p populations of spin packets in slow exchange in a voxel may be considered and the composition of each population may be represented with a mv- ⁇ distribution of spin packets P ⁇ j ⁇ j (D) with parameters ⁇ j and ⁇ j , j ⁇ [1, . . . , N p ]. This amounts to the mixture:
- Finite values of ⁇ j capture the heterogeneity of each population of spin packets as shown in FIG. 3 f . Specifically, a distribution with a sharp peak indicates a population with a highly homogeneous microstructure, and a distribution with a broad peak indicates a highly heterogeneous population.
- Equation (9) provides a generalized expression of the DW signal arising from heterogeneous populations (e.g., different fascicles) of heterogeneous spin packets in each voxel.
- heterogeneous populations e.g., different fascicles
- Cytotoxic brain edemas which occur in ischemic strokes and in traumatic brain injuries are characterized by intracellular water accumulation caused by an increased cell membrane permeability for ions and by ionic pump failure due to energy depletion. This leads to a greater proportion of water molecules inside glial cells, where diffusion is macroscopically isotropic but becomes restricted. This isotropic restricted diffusion may be captured by considering a second distribution with isotropic mode M iso,r 0 , shape parameter ⁇ iso,r and volumic fraction f iso,r .
- the diffusion of water molecules restricted and hindered by a fascicle j may both be represented by a single mv- ⁇ distribution with anisotropic cylindrical M j 0 , shape parameter ⁇ j and volumic fraction f j leading to the signal generation model:
- This model has 6N f +4 free parameters.
- the diffusion of water molecules restricted to the intra-axonal space of a fascicle j and the surrounding hindered extra-axonal molecules may each be represented by a mv- ⁇ distribution with anisotropic cylindrical M j,r 0 (intra-axonal restricted) and M j,hin 0 (hindered) with identical eigenvectors and with shape parameters ( ⁇ j,r , ⁇ j,hin ) and volumic fractions (f j,r , f j,hin ):
- a tortuosity model may be employed to constrain the diffusivities of water molecules inside and around axons resulting in only two additional free parameters per fascicle compared to equation (10): the intra-axonal volume fraction
- v j f j , r f j , r + f j , hin and one additional concentration parameter per fascicle ( ⁇ j,r , and ⁇ j,hin instead of ⁇ j ).
- the parameters of the DIAMOND model at each voxel may be estimated using a maximum a posteriori approach.
- V denotes the image domain
- y denotes the set of N g DW images
- y k i denotes the i th voxel of the gradient image k.
- a variable number N p i of populations of spin packets for each voxel i is considered.
- f ( f 1 i , ... ⁇ , f N Pi i , i ⁇ V ) ⁇ denotes the corresponding fractions of occupancy.
- the tensors D are parameterized in the log-domain by setting
- the parameters ⁇ circumflex over (D) ⁇ MAP may be computed as exp( ⁇ circumflex over (L) ⁇ MAP ).
- prior knowledge about the estimated fractions and shape parameters ⁇ is not considered so that p(f
- prior knowledge about the estimated fractions and shape parameters ⁇ may be considered.
- the noise was assumed to be Gaussian (zero-mean and variance ⁇ 2 ) and independent between images and between voxels, so that:
- the noise may be assumed to have a non-Gaussian distribution.
- the noise may be assumed to have a distribution that is Rician or non-central Chi-squared.
- Parametric models for use with embodiments of the invention may be implemented in any suitable way including any suitable combination of hardware and software, and aspects of the invention are not limited in this respect.
- the DIAMOND estimation algorithm is implemented in C++ and parallelized over the image space.
- numerical optimization (equation (12)) may be achieved with the BOBYQA algorithm described by Powell ( The BOBYQA algorithm for bound constrained optimization without derivatives. In Technical report NA 2009/06 . Department of Applied Mathematics and Theoretical Physics , Cambridge, England), a derivative-free bound-constrained optimization technique.
- BOBYQA is an iterative algorithm. At each iteration, it computes from a set of points a quadratic approximation for the objective function.
- the point giving the largest value for the objective function is replaced by the minimum of the quadratic approximation computed in a trust region. At each iteration the trust region is updated.
- BOBYQA converges faster than the Newton method and is less sensitive to local minima compared to gradient descent algorithms such as conjugate gradient or Levenberg-Marquardt.
- the orientation of the L i 's was parameterized with the Euler angles, as they empirically led to a more efficient optimization.
- Tensors and fractions were initialized and concentration parameters ⁇ 's were initialized to 100 (high compartment homogeneity). Optimization was achieved by gradually increasing the model complexity, from a single stick model to the ball-and-stick to the estimation of the full DIAMOND model.
- the total running time for a typical DWI acquisition with matrix size 128 ⁇ 128 was approximately seven minutes per slice with a Pentium Xeon E5-2687 W processor with eight cores.
- novel parametric models designed for use with some embodiments are configured to be fitted to a set of DWI data having multiple non-zero b-values. Any suitable technique may be used to generate DWI data having multiple non-zero b-values, and embodiments are not limited in this respect.
- the Cube and Sphere (CUSP) gradient encoding scheme described in more detail below may be used to generate the set of DWI data.
- CUSP combines spherical and cubic sampling in q-space, achieving a large number of non-zero b-values with short TE, high SNR and high angular coverage.
- CUSP is based on a modification of a 2-shell HARDI.
- the pulse duration and separation ⁇ and ⁇ of the PGSE sequence are fixed to achieve the b-value of the inner shell (instead of the outer-shell for multi-shell HARDI), which requires a shorter TE and provides a significant SNR boost.
- the gradients of the outer shell have maximally separated gradients orientation with respect to the inner shell but cannot be imaged with the fixed low ⁇ and ⁇ .
- This cube is a cube of constant TE in q-space, in which any gradient can be imaged without modification of ⁇ and ⁇ but by appropriate application of the gradient system.
- CUSP enables imaging of multiple b-value with low TE, high SNR and high angular coverage.
- any other suitable gradient encoding scheme may alternatively be used to generate a set of diffusion-weighted images having multiple non-zero b-values.
- some embodiments are directed to application of a novel diffusion model to diffusion-weighted data having multiple non-zero b-values.
- the model is motivated by biophysical considerations of the microstructure giving rise to the DW signal and that can be applied in clinical practice. Measurements of the signal arising from 3-D spin packets within each voxel were considered and each population of 3-D spin packets was characterized by estimation of a peak-shaped statistical distribution of diffusion tensors, as described above in connection with FIG. 3 f.
- the peak-shaped matrix-variate Gamma distribution P ⁇ , ⁇ was considered, which enables computation of an analytical solution to equation (4).
- the matrix-variate Gamma distribution generalizes the Wishart distribution by allowing a non-integer number of degrees of freedom.
- the number of Wishart components (N>100) was linked to the discretization resolution of the fascicle orientation distribution function (fODF), irrespective of the number of underlying tissue compartments present in each voxel. Importantly, this corresponds to a model of the signal.
- DIAMOND focuses on capturing the distributions of 3-D diffusivities arising from each tissue compartment (see FIG. 3 ) and corresponds to a model of the tissues. It requires the estimation of the number of tissue compartments, i.e., the number of mv- ⁇ components. This was achieved by assessing the generalization error of models of increasing complexity in each voxel. Unlike previous models, DIAMOND requires the acquisition of multiple non-zero b-values to disentangle the decay curves arising from each tissue compartment and provides information at various diffusion scales.
- the diffusion data is acquired using the CUSP gradient scheme, which images a large number of different b-values with uniform angular coverage and low TE, providing a substantial SNR boost compared to a multi-shell HARDI acquisition.
- the parameters of DIAMOND provide a macroscopic description of the tissue microstructure in each compartment.
- the concentration parameter ⁇ of P ⁇ , ⁇ captures the overall compartment's heterogeneity.
- a mv- ⁇ component with a small ⁇ describes the presence of heterogeneous 3-D diffusivities in the compartment, suggesting a heterogeneous microstructure.
- a mv- ⁇ component with a large ⁇ indicates an homogeneous microstructure.
- ⁇ captures any heterogeneity that is consistent with an (oriented) 3-D compartment. Such heterogeneity may result from heterogeneity in fascicle orientation, in axonal diameter, in axonal density, or from undulation of axons.
- Modeling together multiple sources of heterogeneity is not a limitation. There are many possible sources of heterogeneity at different diffusion scales, and it is not clear whether they can be captured separately when using a clinical scanner with long ⁇ and ⁇ and clinically compatible scan times.
- the NODDI approach suggested that the fascicle dispersion and the intra-volume cellular fraction (ICVF) could be specifically assessed by relying on a fixed representation of a WM fascicle throughout the brain.
- the simulations described herein illustrate that, when the simulated microstructure differs from the prefixed fascicle microstructure, the diffusion profile estimated by NODDI substantially deviates from the true profile, even without noise.
- the techniques described herein consider the presence of multiple fascicles per voxel, e.g., the presence of multiple anisotropic compartments.
- the evaluation of the DIAMOND model described herein shows that the estimated number of fascicles and the estimated fascicle orientations match the known anatomy, both with high-resolution and high-SNR DWI and with an acquisition with a moderate number of DW images achievable in clinical practice.
- the results of the DIAMOND model indicate that the fascicle orientations can be estimated with b-values b ⁇ 3000 s/mm 2 .
- estimation of the concentration parameter ⁇ of the matrix-variate Gamma distribution may provide an important marker of abnormal tissue. As discussed further below in connection with FIG.
- this parameter was different between normal and abnormal tissue in TSC, and an increased heterogeneity along the fascicle located in a tuber in a TSC patient was observed. These observations may reflect heterogeneous myelination or heterogeneous mixture of glial cells as observed in mice models of TSC.
- DIAMOND also provides the fraction of unrestricted water diffusion. As discussed further below, increased unrestricted diffusion was observed in the region of the tuber, which might reflect an increased extra-cellular space, the presence of perivascular spaces, or the presence of giant cells typically observed in TSC brain specimens.
- DIAMOND and NODDI were compared by generating realistic synthetic diffusion data with Monte-Carlo simulations using the Camino toolkit (200000 walkers, 5000 time points). Two axonal geometries were considered: 1) aligned cylinders of varying radii (1 ⁇ m to 10 ⁇ m) and 2) cylinders crossing at 45°.
- NODDI parameters were estimated using the publicly available NODDI toolbox (http://cmic.cs.ucl.ac.uk/mig/). The estimated diffusion profiles of DIAMOND and NODDI were plotted and compared (mean error and standard deviation over the 100 voxels). Variations of DIAMOND's and NODDI's model parameters for increasing axonal radii were investigated.
- Voxels with various axonal orientation dispersion were also simulated.
- 10000 cylinders were simulated with orientations drawn from a Watson distribution with increasing dispersion indices.
- FIG. 6 shows the diffusion profiles of DIAMOND and NODDI computed from the Monte-Carlo simulations.
- the parameters of each diffusion model were estimated using the CUSP65 gradient encoding scheme.
- the average was computed over 100 repetitions of the simulations. The standard deviation over the 100 repetitions is reported as the shaded portion surrounding the lines.
- the dashed line shows the ground truth.
- FIGS. 6A and 6B illustrate results for simulations with cylinders of radius 1 ⁇ m oriented along the z-axis.
- FIGS. 6C and 6D illustrate results for simulations with cylinders of radius 10 ⁇ m oriented along the z-axis.
- FIGS. 6C and 6D show that when the simulated microstructure differs from NODDI's prefixed fascicle response function, NODDI's resulting diffusion profile significantly deviates from the ground truth, even in the noise-free case, as shown in FIG. 6C .
- FIGS. 6C, 6D illustrate results for simulations with crossing cylinders.
- FIGS. 6E and 6F show the substantial error of NODDI in voxels with crossing fascicles. This is an important limitation since crossing fascicles occur in 60% to 90% of the voxels in the human brain. In contrast, the diffusion profile is better captured with DIAMOND.
- FIG. 7 illustrates variations of DIAMOND and NODDI parameters for various microstructures.
- NODDI variations of the axonal radii are captured by variations of the intracellular volume fraction (ICVF), although a constant ICVF was simulated in CAMINO.
- DIAMOND changes in axonal radii are reflected in the compartment's cRD while other parameters (heterogeneity and cAD) remain approximately constant. These changes in cRD are consistent with the known physical behavior of water molecules diffusing more freely in larger axons.
- the dispersion index (ODI) and the intra-cellular volume fraction (ICVF) parameters are reported.
- the variability of the curves show the high sensitivity of the underlying optimizer to local minima.
- Increasing axonal radius is characterized by a decreasing ICVF, as shown in FIG. 7A
- a fixed ICVF was simulated.
- Increasing dispersion is correctly characterized by an increasing ODI index, as shown in FIG. 7B .
- HEI heterogeneity index
- FIG. 7B shows that NODDI correctly captures the increased axonal dispersion via the ODI parameter, while a slight decrease in ICVF is observed.
- DIAMOND captures the increased axonal dispersion as an increased heterogeneity of 3D diffusivities (HEI), which is an expected behavior.
- HEI 3D diffusivities
- the cRD remains constant with increasing dispersion while the cAD decreases. This is consistent with the known physical behavior of water molecules whose diffusion endures more restrictions along the average fascicle orientation when the dispersion increases.
- DIAMOND The performance of DIAMOND was compared to various diffusion models with in-vivo acquisitions by assessing their generalization error (GE), which quantifies the capability of each model to accurately predict the DW signal for unobserved gradient directions and strengths, and therefore reflects how well each model captures the mechanisms underlying the signal generation. Acquisitions were carried out using a Siemens 3T Trio scanner with a 32 channel head coil and a pulsed-gradient spin echo (PGSE) DWI sequence with echo-planar imaging (EPI) readout. Eddy current distortion was minimized by utilizing a twice-refocused spin echo sequence. A CUSP90 scheme was used.
- GE generalization error
- the gradient orientations were compensated for the rotation component of the transformation for each image.
- FIG. 8 shows a comparison of five diffusion models with in-vivo data by assessment of their generalization error.
- FIG. 8A illustrates a T1-weighted image of the diffusion signal.
- FIG. 8B shows the results when DTI is used to predict the diffusion signal shown in FIG. 8A .
- DTI is a poor predicator of the diffusion signal, likely because DTI does not account for the non-monoexponential decay and assumes a single compartment per voxel.
- FIG. 8C shows the results when NODDI is used to predict the diffusion signal.
- NODDI provides a lower generalization error than DTI in regions of crossing and close to the cortex because it models the fascicle dispersion and accounts for freely diffusing water.
- FIG. 8D shows the results when the 1T+iso model is used to predict the diffusion signal. As shown, estimation of all the parameters of the 1T+iso model ultimately enables better prediction of the signal compared to NODDI.
- FIG. 8E shows the results when the 1DIAMOND+iso model is used to predict the diffusion signal. As shown, accounting for the heterogeneity of 3D diffusivities (DIAMOND) slightly improves the generalization error in regions of crossings.
- FIG. 8E shows the results when the DIAMOND+iso model is used to predict the diffusion signal. As shown, accounting for each fascicle in each voxel while modeling each compartment heterogeneity provides ultimately the lowest generalization error. Overall, the results show that DIAMOND+iso better predicts diffusion measurements not included in the estimation, supporting the fact that the DIAMOND model better captures the underlying diffusion decay.
- DIAMOND reconstruction was achieved from high-resolution and high SNR super-resolved DWI.
- the underlying high-resolution isotropic DW images were reconstructed at 1 ⁇ 1 ⁇ 1 mm 3 using a quantitative super-resolution technique.
- the parameters of the DIAMOND model were then estimated at each voxel.
- FIG. 9 shows the DIAMOND reconstruction from high-resolution super-resolved DWI.
- FIG. 9A shows that the estimated number of fascicles at each voxel estimated with the 0.632 bootstrap approach matches the known anatomy. For example, as shown no fascicles were detected in the ventricules (i), a single fascicle was detected in the body of the corpus callosum (ii) and in the corticospinal tracts (iii) and up to three fascicles were detected in the corona radiata (iv).
- FIGS. 9B-E show fractions of occupancy estimated by DIAMOND for respectively the unrestricted water diffusion and each of the three fascicles. In particular, FIG. 9B illustrates that the amount of cerebrospinal fluid is well captured by the fraction of free water.
- FIGS. 9F-H show the estimated fascicle orientations by DIAMOND.
- FIGS. 9F-H report the orientation of the mode of each mv- ⁇ distribution.
- FIG. 9F shows a coronal slice of the DIAMOND model super-imposed on the T1-weighted image.
- FIG. 9G shows that DIAMOND correctly captures three crossing fascicles in the corona radiata.
- FIG. 9H shows that DIAMOND well captures the projection of the fascicles into the grey matter of the cortex.
- FIGS. 9I-M show the maps of the concentration parameter of the mv- ⁇ distribution describing each compartment, reflecting the intra-compartment homogeneity (ICHO).
- FIG. 9I shows an axial slice of the reference T1-weighted image.
- FIG. 9J shows the logarithm of the concentration parameter for the unrestricted water diffusion compartment.
- FIGS. 9K-M show the logarithm of the concentration parameter for each of the three fascicles. The logarithm was used in order to enhance the contrast. Larger values of ⁇ [1, ⁇ ] (white) indicate a sharper peak-shaped distribution, and therefore an increased microstructure homogeneity.
- TSC Tuberous Sclerosis Complex
- Data acquisition was conducted using a protocol approved by the Institutional Review Board (IRB). DIAMOND reconstruction was used and both the estimated fraction of unrestricted water diffusion and the concentration parameter of the matrix-variate Gamma distributions were investigated.
- FIG. 10 shows that DIAMOND may provide novel markers of abnormal tissues in disease. Diffusion-weighted data was acquired using the CUSP65 acquisition scheme, described above, and DIAMOND reconstruction was used to model diffusion in the brain of a TSC patient.
- FIG. 10A illustrates T1-weighted (T1W) and T2-weighted (T2W) images of a TSC brain. The cortical tubers are characterized by an hypo-intensity (dark) on T1W and an hyper-intensity (bright) on T2W.
- FIG. 10B shows that the estimated fascicle orientations successfully matches the known anatomy, while a single CUSP65 scan with 65 directions was acquired.
- FIG. 10C shows the estimated fractions of occupancy (top row) and concentration parameter of the matrix-variate Gamma distributions (bottom row) for the unrestricted diffusion (f iso ; ⁇ iso ) and for the fascicle of larger fraction of occupancy (f 0 ; ⁇ 0 ), indicating that these parameters may provide a novel marker of abnormal tissue.
- an increased fraction of unrestricted water diffusion (i) and a decreased intracompartment homogeneity (ICHO) along the fascicle (ii) in the region of the tuber are observed.
- ICHO intracompartment homogeneity
- FIG. 11 shows an illustrative process for using a generative parametric model to predict a diffusion signal in accordance with some embodiments.
- act 1110 diffusion-weighted data having multiple non-zero b-values is received.
- the diffusion-weighted data may be acquired using any suitable acquisition technique including, but not limited to the CUSP technique described briefly above, and in more detail below.
- the process then proceeds to act 1112 , where a model for predicting the diffusion signal in a voxel is generated.
- a priori information about the tissue microstructure the imaged object in the voxel may be used to generate the model for the voxel, though not all embodiments require the use of such information.
- the model generated in act 1112 is based on the DIAMOND model described herein.
- the model may be any other suitable generative model configured to model multiple tissue compartments, with each compartment being represented by a statistical distribution.
- the process then proceeds to act 1114 , where a new compartment is added to the model, thereby increasing the model's complexity.
- the process then proceeds to act 1116 , where the diffusion data for the voxel is predicted with the generative model.
- the process then proceeds to act 1118 , where it is determined whether the compartment is present in the voxel. This determination may be made in any suitable way, and embodiments are not limited in this respect. For example, in some embodiments, it may be determined whether there was a statistically significant improvement in the prediction of the model compared to the previous iteration of the model before the compartment was added.
- the process continues to iterate adding additional complexity to the model until it is determined in act 1118 that the most recently added compartment is not present in the voxel.
- the order in which additional compartments are added to the model at each iteration may be predetermined.
- the process proceeds to act 1120 , where one or more diffusion parameters for the voxel are output.
- the diffusion parameter(s) may be output in any suitable way, and embodiments are not limited in this respect. For example, in some embodiments, a portion of one or more images based on the diffusion parameter(s) may be created and/or displayed. In other embodiments, information relating to the diffusion parameter(s) may be transmitted to one or more other computers for processing and/or one or more storage devices for storage.
- the process then proceeds to act 1122 , where it is determined whether there are additional voxels to process. If it is determined that there are additional voxels, the process returns to act 1112 , where a new voxel is selected and a model for the newly selected voxel is generated. If it is determined in act 1122 that there are no more voxels, the process ends.
- some embodiments analyze the diffusion signal itself to determine the suitable number of compartments to use in modeling diffusion in the voxel. Due to the generalized nature of the model, this approach relies on the acquired diffusion data to have certain properties that can be used to probe the microstructure of a voxel.
- One of these requirements is that the diffusion data must be acquired using an acquisition scheme that enables the acquisition of diffusion data having at least two non-zero b-values.
- An example of such an acquisition scheme is CUSP, as discussed in further detail below.
- a diffusion-weighted acquisition should achieve a trade-off between acquiring adequate b-values while minimizing the TE to maximize the SNR.
- Cube and SPhere acquisition An illustrative acquisition technique that may be used to acquire diffusion-weighted images having multiple non-zero b-values is called Cube and SPhere (CUSP) acquisition.
- This technique combines aspects of a single-shell HARDI with images in an enclosing cube of constant TE.
- the enclosing cube of the shell is a cube of constant TE, in which gradients with higher b-values can be imaged without increasing the TE, by using gradients with norm greater than one.
- Such an acquisition technique satisfies the requirement for multiple non-zero b-values, enabling the estimation of the complete multi-tensor model.
- High b-values may also be incorporated to allow for better characterization of multi-compartment models.
- images associated with b-values higher than the nominal b-value may be acquired while achieving the same low TE as a single-shell HARDI.
- CUSP acquisition results in a significantly higher SNR, shorter imaging time and potentially lower eddy current distortion than previously reported acquisition techniques.
- the CUSP acquisition technique acquires multiple non-zero b-values by combining a first set of gradients for a single-shell HARDI acquisition at a specified b nominal (e.g., 1000 s/mm 2 ) with a second set of gradients having one or more different b-values and having associated gradient strengths that cause the gradients to lie within an enclosing cube of the inner shell.
- This inner shell employs the b-value providing the desired “optimal” SNR for the diffusion weighted acquisition.
- ADC is the apparent diffusion coefficient of the tissue being imaged.
- the single-shell HARDI provides a full spherical sampling with the desired SNR and TE for the b-value b nominal .
- ⁇ 1, which describes the enclosing cube of the sphere of radius ⁇ g k ⁇ 1, which is also referred to herein as the “cube of constant TE.” Any gradient in this region can be acquired without modifying the TE by selecting the appropriate gradient strength.
- diffusion gradient vectors are selected, wherein at least two of the diffusion gradient vectors are associated with different non-zero b-values.
- the diffusion gradient vectors for the gradient encoding scheme may include a first set of diffusion gradient vectors corresponding to a single-shell HARDI acquisition each having a b-value of b nominal and a second set (e.g., one or more) of diffusion gradient vectors each being associated a b-value different than b nominal .
- the plurality of diffusion vectors in the gradient encoding scheme may include a first set of diffusion gradient vectors corresponding to a single-shell HARDI acquisition.
- the gradient strengths of the gradient vectors in the second set may be determined in any suitable way, with the only constraint that all of the vectors in the second set fall on or inside of the cube of constant TE.
- the gradient encoding scheme may be used to acquire diffusion-weighted measurements.
- an MRI system may be programmed with the determined gradient encoding scheme to control various components of the device to acquire diffusion-weighted images having multiple non-zero b-values.
- the diffusion-weighted measurements may then be used to approximate one or more diffusion-based parameters in a parametric model, as described above.
- FIG. 12 shows a schematic block diagram of an illustrative computer 1200 on which features may be implemented. Only illustrative portions of the computer 1200 are identified for purposes of clarity and not to limit aspects of the invention in any way.
- the computer 1200 may include one or more additional volatile or non-volatile memories, one or more additional processors, any other user input devices, and any suitable software or other instructions that may be executed by the computer 1200 so as to perform the function described herein.
- the computer 1200 includes a system bus 1210 , to allow communication between a central processing unit 1202 , a memory 1204 , a video interface 1206 , a user input interface 1208 , and a network interface 1212 .
- the network interface 1212 may be connected via network connection 1220 to at least one remote computing device 1218 .
- Peripherals such as a monitor 1222 , a keyboard 1214 , and a mouse 1216 , in addition to other user input/output devices may also be included in the computer system, as embodiments are not limited in this respect.
- FIG. 13 illustrates a block diagram of one embodiment of a system 1390 suitable for practicing various techniques described herein.
- System 1390 comprises a magnetic resonance (MR) scanning device 1350 and computer system 1300 .
- MR scanning device 1350 may be any device capable of obtaining MR data and, in particular, capable of acquiring DW-MRI data.
- MR scanning device 1350 may include a magnet 1360 capable of producing a magnetic field of desired strength, and may produce a uniform or gradient magnetic field.
- Magnet 1360 may be of any shape, size and strength and may include multiple magnets of any size, shape and strength.
- MR scanning device 1350 also comprises one or more RF coils 1370 arranged proximate the magnet and adapted to provide RF pulse sequences to an object being scanned and/or to detect NMR signals (e.g., DW-MRI signals) emitted therefrom.
- RF coils 1370 may comprise one or multiple coils arranged in any configuration to perform single coil acquisition or multiple coil acquisition (i.e., parallel MR).
- RF coils 1370 may include independent RF coils for providing RF pulse sequences (excitation coils) and detecting NMR signals (receive coils), or one or more RF coils may be arranged as both an excitation and receive coils. Any configuration of magnet 1360 and RF coil(s) 1370 may be suitable, as the techniques described herein are not limited for use on data obtained from any particular MR scanning device.
- Computer system 1300 may be used to implement one or more techniques described herein.
- Computer system 1300 may include one or more processors 1310 and one or more non-transitory computer-readable storage media (e.g., memory 1320 and one or more non-volatile storage media 1330 ).
- the processor 1310 may control writing data to and reading data from the memory 1320 and the non-volatile storage device 1330 in any suitable manner.
- Processor 1310 may be a processor on any device, for example, a personal computer, a workstation, one or more servers, or may be a processor on-board or otherwise integrated with MR scanning device 1350 , etc.
- the processor(s) 1310 may execute one or more instructions stored in one or more computer-readable storage media (e.g., the memory 1320 , storage media, etc.), which may serve as non-transitory computer-readable storage media storing instructions for execution by processor(s) 1310 .
- Computer system 1300 may also include any other processor, controller, or control unit needed to route data, perform computations, perform I/O functionality, etc.
- computer system 1300 may include any number and type of input functionality to receive data and/or may include any number and type of output functionality to provide data, and may include control apparatus to perform I/O functionality.
- Computer system 1300 may be integrated into MR scanning device 1350 or may be a separate stand-alone computer system, either proximate to or remote from MR scanning device 1350 .
- computer system 1300 may be connected to MR scanning device 1350 over a network, connected to multiple scanning devices or may not be connected to any scanning device at all.
- computer system 1300 may be programmed to control the RF coil(s) according to a desired RF sequence or protocol, or MR scanning device 1350 may have a separate controller to perform excitation and acquisition.
- computer system 1300 may operate on MR data (e.g., DW-MRI data) previously stored on computer system 1300 , may obtain DW-MRI data from some other location, e.g., another computer system, over a network, or may obtain the DW-MRI data via transportable storage medium, etc.
- MR data e.g., DW-MRI data
- computer system 1300 may operate on MR data (e.g., DW-MRI data) previously stored on computer system 1300 , may obtain DW-MRI data from some other location, e.g., another computer system, over a network, or may obtain the DW-MRI data via transportable storage medium, etc.
- MR data e.g., DW-MRI data
- the embodiments can be implemented in any of numerous ways.
- the embodiments may be implemented using hardware, software or a combination thereof.
- the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers.
- processors may be implemented as integrated circuits, with one or more processors in an integrated circuit component.
- a processor may be implemented using circuitry in any suitable format.
- a computer may be embodied in any of a number of forms, such as a rack-mounted computer, a desktop computer, a laptop computer, or a tablet computer. Additionally, a computer may be embedded in a device not generally regarded as a computer but with suitable processing capabilities, including a Personal Digital Assistant (PDA), a smart phone or any other suitable portable or fixed electronic device.
- PDA Personal Digital Assistant
- a computer may have one or more input and output devices. These devices can be used, among other things, to present a user interface. Examples of output devices that can be used to provide a user interface include printers or display screens for visual presentation of output and speakers or other sound generating devices for audible presentation of output. Examples of input devices that can be used for a user interface include keyboards, and pointing devices, such as mice, touch pads, and digitizing tablets. As another example, a computer may receive input information through speech recognition or in other audible format.
- Such computers may be interconnected by one or more networks in any suitable form, including as a local area network or a wide area network, such as an enterprise network or the Internet.
- networks may be based on any suitable technology and may operate according to any suitable protocol and may include wireless networks, wired networks or fiber optic networks.
- the various methods or processes outlined herein may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages and/or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a framework or virtual machine.
- embodiments may be embodied as a computer readable medium (or multiple computer readable media) (e.g., a computer memory, one or more floppy discs, compact discs (CD), optical discs, digital video disks (DVD), magnetic tapes, flash memories, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, or other non-transitory, tangible computer storage medium) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement the various embodiments of the invention discussed above.
- the computer readable medium or media can be transportable, such that the program or programs stored thereon can be loaded onto one or more different computers or other processors to implement various aspects of the present invention as discussed above.
- the term “non-transitory computer-readable storage medium” encompasses only a computer-readable medium that can be considered to be a manufacture (i.e., article of manufacture) or a machine.
- program or “software” are used herein in a generic sense to refer to any type of computer code or set of computer-executable instructions that can be employed to program a computer or other processor to implement various aspects of embodiments as discussed above. Additionally, it should be appreciated that according to one aspect of this embodiment, one or more computer programs that when executed perform methods of embodiments need not reside on a single computer or processor, but may be distributed in a modular fashion amongst a number of different computers or processors to implement various embodiments.
- Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices.
- program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types.
- functionality of the program modules may be combined or distributed as desired in various embodiments.
- data structures may be stored in computer-readable media in any suitable form.
- data structures may be shown to have fields that are related through location in the data structure. Such relationships may likewise be achieved by assigning storage for the fields with locations in a computer-readable medium that conveys relationship between the fields.
- any suitable mechanism may be used to establish a relationship between information in fields of a data structure, including through the use of pointers, tags or other mechanisms that establish relationships between data elements.
- embodiments may be embodied as a method, of which an example has been provided.
- the acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.
Abstract
Description
s k(D)=S 0 e −TE/T2 e −γ
S k =S 0 ∫P(D)exp(−b k D)dD, (3)
denotes the non-monoexponential decaying signal arising from a population of spin packets described by Pκ,Σ(d0=κΣ). Finite values of κj capture the heterogeneity of each population of spin packets as shown in
and one additional concentration parameter per fascicle (κj,r, and κj,hin instead of κj).
denote the parameters of the mv-Γ distribution for each population, and
denotes the corresponding fractions of occupancy. The tensors D are parameterized in the log-domain by setting
to ensure the estimation of positive-definite matrices. The estimation of the model parameters is performed by maximizing:
S k =S 0[f free exp(−b k D free)+f 1 exp(−b k g k T D 1 g k)+f 2 exp(−b k g k T D 2 g k)], (14)
Consequently, increasing the nominal b-value increases the minimum achievable TE, which in turn leads to an exponentially-decreased signal amplitude closer to the noise floor. Considering that the noise amplitude is constant, this signal dropout leads to a lower SNR for each diffusion-weighted (DW) image, regardless of their b-value. This leads to a fundamental trade-off in diffusion imaging: while higher b-values are known to increase the contrast between the DW gradient directions, and therefore to increase the reliability of estimation of orientation of each fascicle, higher nominal b-values also lead to a longer TE and to a lower SNR for each DW image, decreasing the estimation certainty and quality. Ideally, a diffusion-weighted acquisition should achieve a trade-off between acquiring adequate b-values while minimizing the TE to maximize the SNR.
(|g k X |=|g k Y |=g k Z|=1).
Claims (16)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US15/022,343 US10317498B2 (en) | 2013-09-20 | 2014-09-19 | Methods and apparatus for modeling diffusion-weighted MR data acquired at multiple non-zero B-values |
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US201361880473P | 2013-09-20 | 2013-09-20 | |
US15/022,343 US10317498B2 (en) | 2013-09-20 | 2014-09-19 | Methods and apparatus for modeling diffusion-weighted MR data acquired at multiple non-zero B-values |
PCT/US2014/056582 WO2015042416A1 (en) | 2013-09-20 | 2014-09-19 | Methods and apparatus for modeling diffusion-weighted mr data acquired at multiple non-zero b-values |
Publications (2)
Publication Number | Publication Date |
---|---|
US20160231410A1 US20160231410A1 (en) | 2016-08-11 |
US10317498B2 true US10317498B2 (en) | 2019-06-11 |
Family
ID=52689451
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
US15/022,343 Active 2035-06-17 US10317498B2 (en) | 2013-09-20 | 2014-09-19 | Methods and apparatus for modeling diffusion-weighted MR data acquired at multiple non-zero B-values |
Country Status (2)
Country | Link |
---|---|
US (1) | US10317498B2 (en) |
WO (1) | WO2015042416A1 (en) |
Families Citing this family (13)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
SE537064C2 (en) | 2012-05-04 | 2014-12-23 | Cr Dev Ab | Analysis for quantification of microscopic anisotropic diffusion |
WO2014052782A1 (en) | 2012-09-28 | 2014-04-03 | Children's Medical Center Corporation | Diffusion-weighted mri using multiple b-values and constant echo time |
WO2016040260A1 (en) * | 2014-09-09 | 2016-03-17 | The Trustees Of The University Of Pennsylvania | Edema invariant tractography |
EP3081955A1 (en) * | 2015-04-13 | 2016-10-19 | Commissariat A L'energie Atomique Et Aux Energies Alternatives | Mri method for determining signature indices of an observed tissue from signal patterns obtained by motion-probing pulsed gradient mri |
SE1551719A1 (en) | 2015-12-29 | 2016-12-20 | Cr Dev Ab | Method of extracting information about a sample by nuclear magnetic resonance measurements |
CN105809670B (en) * | 2016-02-29 | 2019-07-19 | 上海联影医疗科技有限公司 | Perfusion analysis method |
US10959642B2 (en) * | 2016-08-19 | 2021-03-30 | University Of Utah Research Foundation | Methods and systems of evaluating axonal loss and demyelination |
CN109923426B (en) | 2016-11-09 | 2021-09-03 | Cr发展公司 | Method for performing diffusion weighted magnetic resonance measurements on a sample |
JP6932363B2 (en) * | 2016-12-06 | 2021-09-08 | ダルミヤン,インク. | Methods and systems for identifying brain disorders |
TWI651688B (en) * | 2017-03-17 | 2019-02-21 | 長庚大學 | Method for predicting clinical severity of neurological diseases using magnetic resonance imaging images |
EP3575815A1 (en) * | 2018-06-01 | 2019-12-04 | IMEC vzw | Diffusion mri combined with a super-resolution imaging technique |
WO2022221884A1 (en) * | 2021-04-16 | 2022-10-20 | Beth Israel Deaconess Medical Center, Inc. | Systems and methods for non-selective stimulated echo multislice diffusion imaging |
CN115421086B (en) * | 2022-09-02 | 2023-04-14 | 哈尔滨医科大学 | Incoherent motion tensor magnetic resonance imaging method in super-fusion voxel for accurately analyzing complex histological features of living heart |
Citations (10)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20050007100A1 (en) * | 2003-07-08 | 2005-01-13 | Basser Peter J. | Diffusion tensor and q-space MRI specimen characterization |
US20050068031A1 (en) | 2001-04-06 | 2005-03-31 | Frank Lawrence R. | Method for analyzing mri diffusion data |
US20080272781A1 (en) | 2007-05-03 | 2008-11-06 | Chiang Wen-Yang | Q-space sampling method and diffusion spectrum imaging method employing the same |
US20090096448A1 (en) | 2007-10-15 | 2009-04-16 | Siemens Corporate Research, Inc. | b-Value Optimization for Diffusion Weighted Magnetic Resonance Imaging |
US20110085722A1 (en) | 2009-10-14 | 2011-04-14 | Thorsten Feiweier | Correction of distortions in diffusion-weighted magnetic resonance imaging |
US20120027283A1 (en) * | 2003-03-25 | 2012-02-02 | Imatx, Inc. | Methods for the Compensation of Imaging Technique In The Processing of Radiographic Images |
US20120062229A1 (en) | 2009-05-22 | 2012-03-15 | Cr Development Ab | Method And System For Magnetic Resonance Imaging, And Use Thereof |
US20120194189A1 (en) * | 2011-02-01 | 2012-08-02 | Zhe Phillip Sun | System and Method for Diffusion-modulated Relaxation Magnetic Resonance Imaging |
US20120280686A1 (en) | 2011-05-06 | 2012-11-08 | The Regents Of The University Of California | Measuring biological tissue parameters using diffusion magnetic resonance imaging |
US20150253410A1 (en) | 2012-09-28 | 2015-09-10 | Children's Medical Center Corporation | Diffusion-weighted mri using multiple b-values and constant echo time |
-
2014
- 2014-09-19 US US15/022,343 patent/US10317498B2/en active Active
- 2014-09-19 WO PCT/US2014/056582 patent/WO2015042416A1/en active Application Filing
Patent Citations (10)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20050068031A1 (en) | 2001-04-06 | 2005-03-31 | Frank Lawrence R. | Method for analyzing mri diffusion data |
US20120027283A1 (en) * | 2003-03-25 | 2012-02-02 | Imatx, Inc. | Methods for the Compensation of Imaging Technique In The Processing of Radiographic Images |
US20050007100A1 (en) * | 2003-07-08 | 2005-01-13 | Basser Peter J. | Diffusion tensor and q-space MRI specimen characterization |
US20080272781A1 (en) | 2007-05-03 | 2008-11-06 | Chiang Wen-Yang | Q-space sampling method and diffusion spectrum imaging method employing the same |
US20090096448A1 (en) | 2007-10-15 | 2009-04-16 | Siemens Corporate Research, Inc. | b-Value Optimization for Diffusion Weighted Magnetic Resonance Imaging |
US20120062229A1 (en) | 2009-05-22 | 2012-03-15 | Cr Development Ab | Method And System For Magnetic Resonance Imaging, And Use Thereof |
US20110085722A1 (en) | 2009-10-14 | 2011-04-14 | Thorsten Feiweier | Correction of distortions in diffusion-weighted magnetic resonance imaging |
US20120194189A1 (en) * | 2011-02-01 | 2012-08-02 | Zhe Phillip Sun | System and Method for Diffusion-modulated Relaxation Magnetic Resonance Imaging |
US20120280686A1 (en) | 2011-05-06 | 2012-11-08 | The Regents Of The University Of California | Measuring biological tissue parameters using diffusion magnetic resonance imaging |
US20150253410A1 (en) | 2012-09-28 | 2015-09-10 | Children's Medical Center Corporation | Diffusion-weighted mri using multiple b-values and constant echo time |
Non-Patent Citations (11)
Title |
---|
Cook et al., Optimal Acquisition Orders of Diffusion-Weighted MRI Measurements. Journal of Magnetic Resonance Imaging. 2007;25(5):1051-58. |
International Preliminary Report on Patentability for Application No. PCT/US2014/056582 dated Mar. 31, 2016. |
International Preliminary Report on Patentability for International Application No. PCT/US2013/062230 dated Apr. 9, 2015. |
International Search Report and Written Opinion for Application No. PCT/US2014/056582 dated Dec. 16, 2014. |
International Search Report and Written Opinion for International Application No. PCT/US2013/062230 dated Mar. 11, 2014. |
Kuo et al., Optimization of diffusion spectrum imaging and q-ball imaging on clinical MRI system. NeuroImage. 2008;41(1):7-18. |
Nezamzadeh et al., In-vivo investigation of the human cingulum bundle using the optimization of MR diffusion spectrum imaging. European Journal of Radiology. 2010;75(1):e29-36. |
Peled et al., High b-Value Apparent Diffusion-Weighted Images From CURVE-Ball DTI. Journal of Magnetic Resonance Imaging. 2009;30(1):243-48. |
Scherrer et al., Characterizing Complex White Matter Structure from Cube and Sphere Diffusion Imaging with a Multi-Fiber Model (CUSP-MFM). Proc. Intl. Soc. Mag. Reson. Med. 2011;19:1920. |
Scherrer et al., Parametric Representation of Multiple White Matter Fascicles from Cube and Sphere Diffusion MRI. PLOS ONE. 2012;7(11):e48232. |
Yeh et al., Reduced Encoding Diffusion Spectrum Imaging Implemented With a Bi-Gaussian Model. IEEE Transactions on Medical Imaging. 2008;27(10):1415-24. |
Also Published As
Publication number | Publication date |
---|---|
US20160231410A1 (en) | 2016-08-11 |
WO2015042416A1 (en) | 2015-03-26 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
US10317498B2 (en) | Methods and apparatus for modeling diffusion-weighted MR data acquired at multiple non-zero B-values | |
US10782376B2 (en) | Diffusion-weighted MRI using multiple b-values and constant echo time | |
Scherrer et al. | Characterizing brain tissue by assessment of the distribution of anisotropic microstructural environments in diffusion‐compartment imaging (DIAMOND) | |
Sotiropoulos et al. | Ball and rackets: inferring fiber fanning from diffusion-weighted MRI | |
Scherrer et al. | Parametric representation of multiple white matter fascicles from cube and sphere diffusion MRI | |
Tuch et al. | Diffusion MRI of complex neural architecture | |
Lazar | Mapping brain anatomical connectivity using white matter tractography | |
Alexander et al. | Detection and modeling of non‐Gaussian apparent diffusion coefficient profiles in human brain data | |
AU2010347706B2 (en) | Image processing system | |
US11835611B2 (en) | Isotropic generalized diffusion tensor MRI | |
CN111505553A (en) | Magnetic resonance imaging system and method | |
EP2147330B1 (en) | Image processing method | |
Perrone et al. | D-BRAIN: anatomically accurate simulated diffusion MRI brain data | |
Clayden et al. | Microstructural parameter estimation in vivo using diffusion MRI and structured prior information | |
US10324154B2 (en) | Generalized spherical deconvolution in diffusion magnetic resonance imaging | |
Moss et al. | High fidelity fiber orientation density functions from fiber ball imaging | |
US20230266418A1 (en) | Time efficient multi-pulsed field gradient (mpfg) mri without concomitant gradient field artifacts | |
Prčkovska et al. | Optimal short-time acquisition schemes in high angular resolution diffusion-weighted imaging | |
Jeong et al. | Characterizing fiber directional uncertainty in diffusion tensor MRI | |
Ben Alaya et al. | Comparison analysis of local angular interpolation methods in diffusion MRI | |
Isaev et al. | Improved clinical diffusion MRI reliability using a tensor distribution function compared to a single tensor | |
Wessmark | An Exploratory Approach to Generate Ground Truths of NeuralFiber Bundles | |
Jensen | Estimating cerebral water diffusion metrics from MRI using different model assumptions and sequence configurations. A simulation study. | |
Blommaert et al. | Structural network construction using diffusion MRI | |
Lannan | Validation of MRtrix tractography for clinical use |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
AS | Assignment |
Owner name: CHILDREN'S MEDICAL CENTER CORPORATION, MASSACHUSET Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:WARFIELD, SIMON K.;SCHERRER, BENOIT;TAQUET, MAXIME;SIGNING DATES FROM 20171110 TO 20180605;REEL/FRAME:046331/0001 |
|
STPP | Information on status: patent application and granting procedure in general |
Free format text: NOTICE OF ALLOWANCE MAILED -- APPLICATION RECEIVED IN OFFICE OF PUBLICATIONS |
|
STPP | Information on status: patent application and granting procedure in general |
Free format text: PUBLICATIONS -- ISSUE FEE PAYMENT VERIFIED |
|
STCF | Information on status: patent grant |
Free format text: PATENTED CASE |
|
AS | Assignment |
Owner name: NATIONAL INSTITUTES OF HEALTH (NIH), U.S. DEPT. OF HEALTH AND HUMAN SERVICES (DHHS), U.S. GOVERNMENT, MARYLAND Free format text: CONFIRMATORY LICENSE;ASSIGNOR:BOSTON CHILDREN'S HOSPITAL;REEL/FRAME:061974/0977 Effective date: 20210726 |
|
CC | Certificate of correction | ||
MAFP | Maintenance fee payment |
Free format text: PAYMENT OF MAINTENANCE FEE, 4TH YR, SMALL ENTITY (ORIGINAL EVENT CODE: M2551); ENTITY STATUS OF PATENT OWNER: SMALL ENTITY Year of fee payment: 4 |